Discuss how Einstein's theory of gravitation reduces to Newton's in the limit of weak fields. Your answer should include discussion of: (a) the field equations; (b) the motion of a point particle; (c) the motion of a pressureless fluid.

[The metric in a weak gravitational field, with Newtonian potential $\phi$, may be taken as

$$d s^{2}=d x^{2}+d y^{2}+d z^{2}-(1+2 \phi) d t^{2} .$$

The Riemann tensor is

$$\left.R_{b c d}^{a}=\Gamma_{b d, c}^{a}-\Gamma_{b c, d}^{a}+\Gamma_{c f}^{a} \Gamma_{b d}^{f}-\Gamma_{d f}^{a} \Gamma_{b c}^{f}\right]$$